The present invention is directed to a wavefront sensor and more particularly to a wavefront sensor for ophthalmic applications.
It is known in astronomy to detect wavefront aberrations caused by the atmosphere through the use of a Hartmann-Shack detector. Such detection is disclosed, e.g., in D. M. Alloin and J. M. Mariotti, eds., Adaptive Optics for Astronomy, Dordrecht: Kluwer Academic Publishers, 1994. More recently, such a technique has been used to detect wavefront aberrations in the human eye for such purposes as intraocular surgery and contact lens fabrication. Such detection is disclosed, e.g., in Liang et al, xe2x80x9cObjective measurement of wave aberrations of the human eye with the user of a Hartmann-Shack wave-front sensor,xe2x80x9d Journal of the Optical Society of America, Vol. 11, No. 7, July, 1994, pp. 1-9, the disclosure of which is hereby incorporated by reference in its entirety into the present disclosure.
That technique will be summarized with reference to FIG. 1. A beam of light from a laser diode or other light source is directed toward the pupil and is incident on the retina. Because the retina is highly absorbing, a beam on the order of four orders of magnitude dimmer than the original beam is reflected by the retina and emerges from the pupil. Typically, the incoming and emergent light follow a common optical path; the incoming light is brought into the common optical path with a beamsplitter.
The emergent beam is applied to a Hartmann-Shack sensor to detect the aberrations. Such a detector includes an array of lenslets that break up the light into an array of spots and focus the spots onto a charge-coupled detector or other two-dimensional light detector. Each spot is located to determine its displacement xcex94 from the position which it would occupy in the absence of wavefront aberrations, and the displacements of the spots allow reconstruction of the wavefront and thus detection of the aberrations through known mathematical techniques.
Improvements to the technique of Liang et al are taught in J. Liang and D. R. Williams, xe2x80x9cAberrations and retinal image quality of the normal human eye,xe2x80x9d Journal of the Optical Society of America, Vol. 4, No. 11, November, 1997, pp. 2873-2883 and in U.S. Pat. No. 5,777,719 to Williams et al. The disclosures of that article and of that patent are hereby incorporated by reference in its entirety into the present disclosure. Williams et al teaches techniques for detecting aberrations and for using the aberrations thus detected for eye surgery and the fabrication of intraocular and contact lenses. Moreover, the techniques of those references, unlike that of the Liang et al 1994 article, lend themselves to automation. German published patent application No. DE 42 22 395 A1 teaches a further variation using polarizing optics to control back-scatter from the lenses in the detector setup.
Analysis of the eye presents unique problems and issues not necessarily faced in astronomy. For example, while wavefront sensor systems in astronomy exhibit uniform intensity across their entrance pupil, this is not the case with systems for the eye. The eye, unlike a telescope, is subject to the Stiles-Crawford effect. That effect is a directional sensitivity of the retina, one manifestation of which is an intensity variation across the pupil of the eye when light is reflected from the retina. It exists because illuminated cones radiate more light back toward the center of the pupil than toward the pupil margin. Also, unlike astronomy, stray light from other sources, such as from corneal reflection, can be introduced into the wavefront sensor from the eye, and such stray light can interfere with the measurement of spot placement.
Other problems unique to the eye have been encountered. For example, a subset of the spots that should be formed in the Hartmann-Shack detector cannot be seen, either because the aberrations are unusually large (e.g., a huge aberration caused by a scar or the like can displace or deform the spot so much that the spot""s origin cannot be determined or the spot leaves the field of view of the detector altogether), or they are occluded by opacities in the eye""s optics or by the pupil. In current wavefront sensors, the loss of any spots frustrates the computation of the wave aberration.
Another problem is that of variable pupil size, as opposed to the fixed pupil of a telescope.
Moreover, there is the issue of real-time operation. Real-time wavefront sensors have been demonstrated in astronomy, but where operation is required at rates typically greater than 300 Hz with closed loop bandwidths greater than 30 Hz. The atmosphere is much too turbulent for real-time compensation at slower rates. On the other hand, present adaptive optics techniques for the eye operate at a very slow rate, less than 0.25 Hz, and do not automatically compute the wave aberration, even with single exposures. Real-time operation is not possible because of the factors described above. Also, these techniques employ relatively long focal length lenslet arrays. Such instruments have high sensitivity to small changes in the slope of the wave aberration at the expense of dynamic range and robustness. Individual spots in the wavefront sensor image often overlap, particularly near the edge of the pupil, making it difficult for automatic centroid spot computation. Such problems can develop especially for a commercial instrument in which operator intervention should be minimized. As a result, these systems cannot measure the wave aberration in a large fraction of human eyes. An optimized wavefront sensor for the eye should therefore properly balance sensitivity and dynamic range, operate in real-time, and be capable of use with a significant fraction of eyes.
The measurement sensitivity of a wavefront sensor for the eye is determined primarily by the focal length of the lenslet array. The smallest measurable wavefront slope is proportional to the focal length. Relatively long focal length (e.g., 97 mm) lenslet arrays used in high sensitivity wavefront sensors for measuring eye wave aberrations typically show a small mean standard deviation of repeated measurements across the pupil of an artificial eye, for example, xcex/487 (at 632.8 nm, the helium-neon laser wavelength) for a 3.4 mm pupil. Moreover, the eye can exhibit a severe wave aberration at the edge of the pupil due to smeared or scarred areas of the eye""s tissue. Thus, such wavefront sensors exhibit more sensitivity than necessary and require an algorithm to hunt/locate the migrating spots.
Another challenge to real-time wavefront sensing in the eye is the spatial homogeneity of the spot of light imaged on the retina. Inhomogeneity, caused, for example, by laser speckle or reflectance variations in the underlying retina, disrupts the accuracy of the spot localization. This problem is exacerbated with the short exposures required for real-time operation.
As a result of the above-noted problems with wavefront sensing in the eye, a robust and real-time sensing technique for the eye is not known in the art.
While many of the above problems have apparently been overcome in astronomy, it will be readily apparent from the foregoing that a need exists in the art for a wavefront sensor capable of handling the unique problems of the eye. It is therefore a primary object of the invention to address such unique problems, which include nonuniform illumination of the pupil due to antenna properties of cones, ocular abnormalities, variable pupil size either among individuals or in the same individual under different levels of illumination, increasing severity of the wave aberration at the edge of the pupil, and spatial inhomogeneity of the retina, which produces centroiding errors.
To achieve the above and other objects, the present invention is directed to a system adapted to overcome such unique problems.
Errors introduced by nonuniform illumination are handled by locating the spots through the following centroiding technique. Once an image is taken, a set of initial boxes is set up on the image. Each initial box is centered around the location where a corresponding spot would be in the absence of wavefront aberration and has a side of length equal to what the inter-spot spacing would be in the absence of wavefront aberration. A first guess of the spot location is produced by finding the intensity centroid of the portion of the image within each initial box. Then a smaller box is drawn, centered on that centroid. The smaller box can be clipped to lie within the initial box. A new centroid is found within that smaller box. That process is iterated until the box size reaches some criterion size, such as a width equal to the full width of half maximum of the diffraction-limited spot. Each step throws away data remote from the centroid found in the previous step, since such data most likely contain noise or systematic errors rather than information useful in locating the spot.
There are two stages used in centroiding the spots. In the first stage, reference boxes are established based on centered reference positions or on the center of the image on the detector (i.e., xe2x80x9cfrom scratchxe2x80x9d). The latter technique makes less of an assumption where boxes are located and decides how far out to go as the process runs according to the known size of the lenslet array and number of lenslets. The boxes in the latter technique can form an irregular array, which can be described as being constructed in rings about a center box with the location of the outer boxes being determined in a center-to-outward direction. The size of the boxes using either technique can be adjusted by a parameter entered by the operator or stored in software, for example, 90% of the actual inter-lenslet spacing or 90% of the area of a box having sides equal in length to the inter-lenslet spacing.
Once these boxes are determined, a technique can be used that locates a centroid within an initial box, centers a smaller sized box on that centroid, followed by locating the centroid again, followed by another smaller box centering, and so on until the diffraction limited box size is reached and the final centroid is determined. Alternatively, a technique can be used that starts with an initial box, finds a centroid within that box, centers a smaller decremented box on that centroid, clips as described above, calculates the next centroid, centers a decremented box again, clips again, and so on, all the while maintaining each centroid within the original box. This process also terminates when the diffraction limited box size is reached and the final centroid is determined.
An additional centroid can be calculated on the entire array to locate the center, which is especially used with longer focal length lenslet arrays. Doing so permits compensation for spot migration, which is compensated for by the center of mass of the entire array. Iteratively centroiding is to be contrasted with previous techniques such as simply using thresholding and simply by doing a center of mass of the entire box. The present invention better finds the center and reduces the effects of radiance caused by the dimmer spots of the centroids. The technique according to the present invention also reduces the effects of stray light because those effects are progressively eliminated.
The embodiment just described includes re-centering and removing pixel operations. In another embodiment according to the invention, the boxes can be shrunk first, then translated, and then clipped to a threshold value of intensity, in which only those pixel values above the threshold will be included in the calculation of the centroid. There can also be a variable threshold per box as the box size is reduced to account for data from different pixels.
The centroiding technique using shrinking boxes overcomes a difficulty found in centroiding without shrinking boxes, namely, errors when there are broad intensity gradients such as caused by the Stiles-Crawford effect.
Ocular abnormalities, such as scars, can result in spots deviated far from where they would be in the absence of wavefront aberration. Such spots can come close to, or even overlap, other spots. In fact, such spots can be displaced so far that they disappear from the field of view of the detector altogether. Other ocular abnormalities, such as occlusions, can absorb light, so that no spot is produced at all. To handle such abnormalities, the present invention provides a technique for wavefront reconstruction in the absence of certain data points. Part of the wavefront reconstruction involves manipulation of a matrix whose rows correspond to displacements of the spots from their positions in the absence of aberration. For spots not producing usable data, the rows can simply be deleted from the matrix, or the values contained in such rows can be extrapolated from neighboring rows.
At the heart of this flexibility is the particular data structure, which is a matrix of Zernike mode number in the columns and centroid displacement number in the rows. The matrix is used to calculate the Zernike coefficients to determine the wave aberration of the eye.
Different criteria can be used for determining whether to omit a centroid or not, such as the standard deviation of the light within a box in the center of mass calculation, a position of a point being outside of a box or in a highly unexpected area within the box, or points being occluded totally by corneal defects. Then based on these omitted response or centroids which can be done on a frame by frame basis if desired, one calculates the Zernike modes.
Variable pupil size can be handled either before or after data are taken. If the variable pupil size is to be handled in the same individual, data can be taken twice. If that is not convenient or possible, data can be taken in a larger pupil radius, and then the centroids in a smaller radius can be located. A renormalization procedure is used to provide a matrix to convert the wavefront reconstruction from the larger radius to the smaller one. The variable pupil size results in a variable number of spots used in wavefront reconstruction, which can be handled by varying the number of Zernike modes used in the reconstruction. The wave aberration is recalculated based on a new radius using software as opposed to changing the actual excluded centroids.
Starting with a valid number of data points, the software can determine a number of Zernike orders, and correspondingly a maximum number of modes that can be accurately calculated. For example, order 0 has mode 1, order 1 has modes 2 and 3, order 2 has modes 4, 5, and 6, etc. Generally, if one calculates particular modes within an order, it is desirable to have all the modes within that order. Therefore, one would not calculate modes 7 and 8, 7 but not 9 and 10 since those are all within the third order Zernike equations. A general rule of thumb for calculating the order is (modes+1)(modes+2)/2. Based on this equation, one sees that beginning with the number of available centroids, that number of centroids is divided by two, yielding the maximum calculable modes.
One can determine the highest order that can be accurately calculated based upon the number of lenslets divided by 2, yielding the number of calculable modes. Then, the highest complete number of modes translates to a particular order. For example, 20 centroids yields 10 Zernike modes, which allows one to accurately compute the third order Zernike equations.
The increasing severity of the wavefront aberration at the edge of the pupil can be dealt with as just described.
Spatial inhomogeneity of the retina can be handled through the following techniques. A light source of short coherence length reduces the problem of speckle caused by interference in light of high coherence. In addition, the inhomogeneity can be averaged out by scanning the illuminating light across a short distance of the retina and de-scanning the emergent light.
The above features allow a wavefront sensor according to the present invention to provide fast, robust and accurate centroiding, e.g., up to 50 Hz.